The equation of the chord of the circle ${a}^{2} + {y}^{2}-4x=0$, whose mid point is $\left( 1,0 \right) $ is

The given circle equation x^2 + y^2 - 4x = 0 has a center at (2, 0) and the midpoint of the chord is (1, 0). The slope of the line segment connecting the center (2, 0) and the midpoint (1, 0) is 0, which means this line is horizontal. Since the line from the center to the midpoint of a chord is perpendicular to the chord itself, the chord must be a vertical line. Therefore, the equation of the chord is the vertical line passing through (1, 0), which is x = 1.

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